Beauville, Arnaud
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Limits of the trivial bundle on a curve

We attempt to describe the rank 2 vector bundles on a curve C which are
specializations of the trivial bundle. We get a complete classifications when C
is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit
vector bundles are decomposable. We give examples of indecomposable limit
bundles for some special curves.